The course deals with weak convergence of probability measures on Polish spaces. Here the principal examples of Polish spaces are the space C = C[0,1] of continuous trajectories and the space D = D[0,1] of cadlag trajectories. Main topics: - Portmanteau and mapping theorems - Tightness and Prokhorov theorem - Functional central limit theorems on C and D - Empirical distribution functions and the Brownian bridge - Weak convergence on D[0, infinity)
Syllabus
The course is
- given in the second half of spring